Let $F_q$ be a finite field of order $q$. Let $A$ be a finite dimensional algebra over $F_q$ of dimension $d$ and let $e < d$ be some positive integer. Then what is the number of sub-algebras of $A$ of dimension $e$?
For example consider the following algebra of $3 \times 3$ matrices:
$\left\{ \begin{pmatrix}a_0&a_1&b\\0&a_0&0\\0&c&d\end{pmatrix} \text{ $:$ $a_0, a_1, b, c, d \in F_q$} \right\}$ I want to count the number of 3-dimensional subalgebras of this algebra.
If $A$ is a field of prime dimension $p$ over $F_q$, then it has exactly two subalgebras. If instead $A=(F_q)^p$ is a direct product of $p$ copies of $F_q$, then it has many more than $2^p-1$ subalgebras, many of which have the same dimension.
It follows from this that knowing just $d$, $w$ and $q$ one cannot answer your questoin.